As we are not told in what year Mr. Jasper Bullyon made the generous
distribution of his accumulated wealth, but are required to find the
lowest possible amount of money, it is clear that we must look for a
year of the most favourable form.
There are four cases to be considered--an ordinary year with fifty-two
Sundays and with fifty-three Sundays, and a leap-year with fifty-two and
fifty-three Sundays respectively. Here are the lowest possible amounts
in each case:--
313 weekdays, 52 Sundays £112,055
312 weekdays, 53 Sundays 19,345
314 weekdays, 52 Sundays No solution possible.
313 weekdays, 53 Sundays £69,174
The lowest possible amount, and therefore the correct answer, is
£19,345, distributed in an ordinary year that began on a Sunday. The
last year of this kind was 1911. He would have paid £53 on every day of
the year, or £62 on every weekday, with £1 left over, as required, in
the latter event.